SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Invited Talk

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Functional-analytic aspects of DAEs

R. März

Abstract
The great progress of the theory of PDEs during the twentieth century, both the analytical and the numerical parts, are unthinkable without the achievements and contributions of the functional analysis emerging at that time. In contrast, so far, the impact of functional-analytic ideas in the theory of DAEs is weak. The field of DAEs is widely dominated by standard ODE tools and geometric approaches. The functional-analytic character of DAEs is hardly developed so far; by now, an adequate sophisticated characterization has not been accomplished. What's more, one might find seemingly conflicting assertions. We consider operators associated with linear and nonlinear DAEs acting in various Banach and Hilbert spaces. We ask for settings such that the DAE operator becomes bounded or closed with dense domain. Then we investigate whether a DAE operator has a closed range and whether it is a Fredholm operator. Furthermore, we discuss consequences for the approximate solution.

Organized by         Universidad de Valladolid     IMUVA